Prepare two 9 by 2-inch round pans; preheat the oven to 350F.
Sift together the flour, baking powder, baking soda, salt, cocoa and cinnamon into a medium bowl.
In the bowl of a stand mixer fitted with the flat beater, beat the granulated sugar, brown sugar, oil, eggs and vanilla on medium speed for 1 minute, or until well blended. Add the flour mixture and beat on low speed for about 20 seconds, just until incorporated. Add the carrots and beat for another 12 seconds. Scrape the batter into the prepared pans and smooth the surfaces evenly with a small offset spatula. Each will be just under half full.
Bake for 45 to 55 minutes, or until a wire tester inserted in the centers comes out clean and the cakes spring back when pressed lightly in the centers. The cakes should just start to shrink from the sides of the pans. Let the cakes cool in the pans on a wire rack for 10 minutes. Run a small metal spatula between the sides of the pans and the cakes, pressing firmly against the pans, and invert the cakes onto wire racks that have been coated lightly with nonstick cooking spray. Cool completely before frosting.